A102644 A006530(x)=2 is a local minimum if x=2^n. Running downward with argument x started at 2^n, the largest prime divisor should increase. The value of first peak is a(n).

2, 3, 7, 13, 31, 61, 127, 127, 73, 1021, 89, 4093, 8191, 16381, 151, 257, 131071, 131071, 524287, 1048573, 337, 683, 178481, 16777213, 1801, 8191, 262657, 1877171, 2089, 46684427, 2147483647, 2147483647, 599479, 3360037, 6871947673, 283007

Offset: 1

Author

Labos Elemer, Jan 21 2005

Keywords

• nonn

Comments

We may call these terms "downward-zenith-primes" belonging to 2^n-s. They do not exceed previous-primes before 2^n [A014234(n)].

Examples

			n=20: 2^20=1048576; the largest prime divisors for arguments if running downward from 2^20 are as follows: {2,41,524287,1048573,73}.
The first lower peak before argument 2^20=1048576 is a(20)=1048573.
n=1: a(1)=2 the peak equals the central value because there are no prime divisors>0 below n=2^1=2.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A006530, A102640, A102641, A102642, A102643, A014234.

Programs

Mathematica

Table[2 + Total@ TakeWhile[Differences@ Map[FactorInteger[#][[-1, 1]] &,
TakeWhile[Range[2^n, 2^n - 20, -1], # > 0 &]], # > 0 &], {n, 36}] (* Michael De Vlieger, Jul 31 2017 *)